I don't
remember enough of the constants to figure out what sort of
acceleration a gradient of, say, 200 V/cm imparts to a free
electron....
I think you need study a broken tube to find the distance from the
cathode first.
I have looked at broken tubes, and I've seen cathode-plate distances
everywhere from about 0.5mm up to about 1cm, depending on the tube.
(That's ignoring special cases such as CRTs.)
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